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Ivan
3 years ago
14

Find dyldx. 3. y=2x sin(3x)

Mathematics
1 answer:
vredina [299]3 years ago
6 0

Answer:

\large\boxed{\dfrac{dy}{dx}=2\sin(3x)+6\cos(3x)}

Step-by-step explanation:

\dfrac{dy}{dx}=(2x\sin(3x))'\\\\\text{use}\ \bigg(g(x)\cdot f(x)\bigg)'=g'(c)f(x)+g(x)f'(x)\\\\\text{and}\ \bigg(f(g(x))\bigg)'=f'(g(x))\cdot g'(x)\\\\\dfrac{dy}{dx}=(2x)'(\sin(3x))+(2x)(\sin(3x))'\\\\\dfrac{dy}{dx}=2\sin(3x)+(2x)(\cos(3x)\cdot(3x)')\\\\\dfrac{dy}{dx}=2\sin(3x)+2x\cos(3x)\cdot3\\\\\dfrac{dy}{dx}=2\sin(3x)+6\cos(3x)

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I want the answer and way to do this problem.
user100 [1]

∠ABC = ∠CDA (given)

∠BCA = ∠DAC (given)

CA = AC (common side)

ASA congruence criterion = when two angles of two triangles are equal and their included side is also equal, we can consider those triangles to be congruent to each other.

Since two angles in triangle △ABC and△CDA are equal and since their included side is also equal we can conclude that they are congruent.

Therefore, △ABC ≅ △CDA under the ASA congruence criterion.

8 0
3 years ago
Find the equation of the line perpendicular to y =<br> 3x + 6 and containing the point (-9,-5).
neonofarm [45]

The equation of the line perpendicular to y =  3x + 6 and containing the point (-9,-5) is y = \frac{-1}{3}x - 8

<em><u>Solution:</u></em>

Given that line perpendicular to y =  3x + 6 and containing the point (-9, -5)

We have to find the equation of line

<em><u>The slope intercept form is given as:</u></em>

y = mx + c  ------ eqn 1

Where "m" is the slope of line and "c" is the y - intercept

<em><u>Let us first find the slope of line</u></em>

The given equation of line is y = 3x + 6

On comparing the given equation of line y = 3x + 6 with eqn 1, we get,

m = 3

Thus the slope of given equation of line is 3

We know that <em>product of slopes of given line and slope of line perpendicular to given line is equal to -1</em>

Slope of given line \times slope of line perpendicular to given line = -1

3 \times \text{ slope of line perpendicular to given line }= -1

\text{ slope of line perpendicular to given line } = \frac{-1}{3}

Let us now find the equation of line with slope m = \frac{-1}{3} and containing the point (-9, -5)

Substitute m = \frac{-1}{3} and (x, y) = (-9, -5) in eqn 1

-5 = \frac{-1}{3}(-9) + c\\\\-5 = 3 + c\\\\c = -8

<em><u>Thus the required equation of line is:</u></em>

Substitute m = \frac{-1}{3} and c = -8 in eqn 1

y = \frac{-1}{3}x - 8

Thus the required equation of line perpendicular to given line is found

6 0
3 years ago
If (x+5) and (x+2) are the factors, then the solutions are______ and ______. *
tangare [24]
X = -2 and -5
You can set both equal to 0 to find the answers.
5 0
2 years ago
If your salary is $42,500 and your federal income taxes are 10% of your salary, how much money will you owe this year in federal
Zarrin [17]
I'm assuming that the salary is for the whole year. If it is not, do tell me. 
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6 0
2 years ago
Kobe has collected 750 football cards and 660 baseball cards. He wants to divide them into piles so that each pile has only one
Harrizon [31]

Answer: 30 cards

Step-by-step explanation:

To find the greatest possible number of cards in each pile such that there is the same number of cards in each​ pile we need to find the greatest common factor of 750 and 660.

Using Euclid division method , we have

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Hence, the greatest common factor of 750 and 660 = 30

Thus, there will be 30 cards in each pile.

4 0
3 years ago
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